It is a lot of fun to read all of this, so I cannot resist commenting again.
Actually most instructors (even sidemount instructors) here in my area would agree with Ragnar. They just saw a demand from the customers and are good businesspeople, but they are not convinced and do not always look convincing.
Those people in the criticized vids sometimes have had hundreds (or even thousands) of backmount dives before becoming sidemount instructors on a weekend.
Some of the discussions developing from that are instructive, some are only frustrating and repetitive.
But I can count on a few things. One of them: nobody here will underestimate the importance of proper gas management.
Most overestimate it!
Even in those monkey diving classes 'rule of thirds' is often taught as the lowest safety margin acceptable.
Most sidemounters share dives with single tank backmounters calculating on '50 Bar is enough'.
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On the other hand the ideas that backmounters have about sidemount safety sometimes seem hilarious.
While sidemounters learn to finish any dive with significant gas losses (that could never happen on normal recreational dives), backmounted doubles are mostly thought of as 'failure proof'.
The unrealistic option of really having to resort to tank feathering is often turned into a problem by people - who have next to no experience in sidemount and seem to me to have never used stages properly in backmount.
I have seen people doing 40 minute shallow water dives with 20 minutes of tank feathering on one side without me even realizing it and did the same thing myself with a purposefully disabled regulator.
But this is a totally unrealistic training option for a recreational diver, nothing but a funny game with 'other peoples risks'.
The option of tank feathering is something from the backmount world, where you cannot see what is happening with your first stages, that is still influencing sidemount.
Most situations that would lead to shutting off one regulator in backmount will only make you shrug and grumble a bit in a sidemount configuration (e.g. broken regulator hose o-ring, etc...).
You can always switch to the other side to abort the dive and if you really miscalculated that much and have to use that to its limit, you still have the option of using most of the gas from the failing side (even if you are not trained to use tank feathering, breathing from a failing regulator (with a nearly turned off valve) is not that hard, if you have to and since there is no need to panic there is a good chance to cover a few vertical meters without damaging your ears or worse).
Of course one can only think about making challenging dives sidemounted if he is much better controlled than seen in the videos. But most seem to be after couple of training dives and a bit of equipment tweaking.